I think hipmummy and leesa's suggestions combined could work.

Does DS see your ILs undermining you? If so, this could be encouraging his behaviour, but regardless, that has to stop, and I think it's a great idea if DS witnesses that.

I'd say he's also kicking up about the disruption in his life, so maybe some extra one-on-one time might be needed.

Lastly - I have to say my DS gets very upset when he gets into trouble so it is fairly easy to impress him - but what would happen if, say when your DS spits, you stood up very straight and tall and in a very firm and loud voice said something like "EXCUSE ME, how dare you do that? That is not nice, Mummy never spits at you. Don't you EVER do that again." Of course the facial expression combined with voice tone is key here...for me, it's all about conveying the expression with my eyes as well as my face. I channel my old headmistress!